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If ∆FEC≅∆GDB, ∠1=∠2. Prove that ∆ADE~∆ABC

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If ∆FEC≅∆GDB, ∠1=∠2. Prove that ∆ADE~∆ABC

    • Posted by Veena Katti 6 years, 11 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 6 years, 11 months ago

    Given : ∆ FEC ≅ ∆ GBD  , 

    SO From CPCT

    WE GET,

    BD = CE ----------------- ( 1 )

    ALSO GIVEN : ∠ 1 =  ∠ 2  ,

    SO FROM BASE 

    ANGLE THEOREM IN ∆ ADE

    WE GET

    AD  =AE ------------------------ ( 2 ) 

    From equation 1 and 2 we get

    ADBD = AECE , So from converse of B.P.T. we get

    DE | | BC

    THEN ,

    ∠ 1  = ∠ 3                                  
    ( CORRESPONDING ANGLES AS DE  | | BC AND AB IS TRANSVERSAL LINE )

    AND

    ∠ 2  = ∠ 4                                  ( CORRESPONDING ANGLES AS DE  | | BC AND AC IS TRANSVERSAL LINE )

    FROM ABOVE TWO EQUATIONS WE CAN SAY THAT :

    ∆ ADE ~ ∆ ABC        ( ByAArule )
    ( Hence proved )

    1Thank You

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